Includes bibliographical references (pages 203-212) and index

Discusses the invention of numbers, including the daily applications, concepts, and the metric and American systems of measurement. One of the most fundamental concepts influencing the development of human civilization is numbers. While societies today rely on their understanding of numbers for everything from mapping the universe to running word processing programs on computers to buying lunch, numbers are a human invention. Babylonian, Roman, and Arabic societies devised influential systems for representing numbers, yet the story of how numbers developed is far more complicated. Concepts such as zero, negative numbers, fractions, irrational numbers, and roots of numbers were often controversial in the past. Numbers deals with the development of numbers from fractions to algebraic numbers to transcendental numbers to complex numbers and their uses. The book also examines in detail the number pi, the evolution of the idea of infinity, and the representation of numbers in computers. The metric and American systems of measurement as well as the applications of some historical concepts of numbers in such modern forms as cryptography and hand calculators are also covered. Illustrations, thought-provoking text, and other supplemental material cover the key ideas, figures, and events in the historical development of numbers

Acknowledgments -- Introduction: Number and imagination -- Numbers for computation: First problems -- Early counting systems -- Mesopotamian education -- Mesopotamian number system -- Mesopotamian mathematics homework -- Egyptian number system -- Problem from the Ahmes papyrus -- Mayan number system -- Chinese number system -- Problem from the nine chapters -- Our place value number system -- Explaining the new system -- Analytical engines: Calculators, computers, and the human imagination -- Charles Babbage and the analytical engine -- Early electronic representation of our number system -- Floating-point representation -- Floating-point arithmetic and your calculator -- Why computers? -- Extending the idea of a number: Evolving concept of a number -- Irrational numbers -- Pythagoras of samos -- Irrationality of [radical]2 -- Negative numbers: Ancient mathematical texts from the Indian subcontinent -- Out of India -- Algebraic numbers: Tartaglia, Ferrari, and Cardano -- Girard and Wallis -- Euler and d'Alembert -- Debate over "fictitious" numbers -- Complex numbers: Modern view -- Using complex numbers -- Transcendental numbers and the search for meaning: Dedekind and the real number line -- Problem of infinity: Early insights -- Galileo and Bolzano -- Infinity as a number -- Life and opinions of Tristram Shandy, gentleman -- Georg Cantor and the logic of the infinite: -- There are no more rational numbers than natural numbers -- There are more real numbers than natural numbers -- Russell Paradox -- Resolving the Russell paradox -- Cantor's legacy: Kurt Godel -- Formal languages today -- Alan Turing -- Chronology -- Glossary -- Further reading -- Index